where \(f(\mathbf {x})\)  is an activation function over a set of inputs
\(\mathbf {x}\) , \(W\)  is a weight matrix, and \(y^{\prime }\)  is a guessed
classification label. This model is composed of \(l\)  sequential layers
of neurons \(\lbrace a^{(i)}_{n_i}\rbrace \) , where \(0<i<l\) , and \(n_i\) 
specifies the number of neurons in a given layer \(i\) . Each neuron is
subject to the activation function \(f\) . Additionally, each layer of
neurons has a specified weight matrix \(W^{(i)}\) , which connects the
output from one layer to the input of the next. The components of each
\(W^{(i)}\)  are used as parameters for optimization of the
network.[1]} Figure REF  provides a
schematic for a MLP with a single layer of neurons between the input
and final output.
